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Given the function f(x) = -3x^3 +3x^2+ 3x + 3, which of the following is true?

-It is positive

-It is a cubic function

-The domain is all real numbers.

-It has at most 2 solutions

-it is a polynomial function

By using the graph, the average rate of change of the function f from 2 to 5 is equal to -1.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function f from the graph over the interval [2, 5]:

a = 2; f(a) = 4

b = 5; f(b) = 1

Substituting the given parameters into the average rate of change formula, we have the following;

Average rate of change = (1 - 4)/(5 - 2)

Average rate of change = -3/3

Average rate of change = -1.

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The value of sin A is, 7/25.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

The terminal side of angle A goes through the point (−24/25,7/25) on the unit circle.

Now, By definition we get;

⇒ cos A = - 24/25

⇒ Sin A = 7/25

Thus, The value of sin A is, 7/25.

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Answer:

Step-by-step explanation:-46

The length of the trail on the map would be 3.7 cm when a bike trail is 7.40km.

Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions on the actual figure or object

On a map, 1.00 cm represents 2.00 km.

Let the required length of the trail on the map would be x cm, when a bike trail is 7.40km

As per the information, we can write the ratio would be as:

1.00 cm : 2.00 km = x cm : 7.40km

1/2 = x/7.40

Apply cross-multiplication operation, and we get

x = 7.40/2

x = 3.7

Thus, the required length of the trail on the map would be 3.7 cm.

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For the linear equation y = -3.5x + 50 the graph is plotted with points (0,50) and (14.28,0).

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The linear equation is y = -3.5x + 50.

An arcade deducts 3.5 points from a 50-point game card for each game played.

The graph will represent the x axis as number of games played.

The graph will represent the y axis as points earned.

Substitute the value x = 0 in the equation -

y = -3.5(0) + 50

y = 50

The coordinate point is (0,50).

Substitute the value y = 0 in the equation -

0 = -3.5x + 50

-50 = -3.5x

x = 14.28

The coordinate point is (14.28,0).

Plot both the coordinate points and join the line.

Therefore, the graph is plotted for the linear equation.

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Answer:

7.40

Step-by-step explanation:

4.58+2.82 = 7.40

Answer:

C.

Step-by-step explanation:

The answer is C (-1, 1/2)

Answer: A baker needs to make a dessert for a party. The recipe calls for 1 3/4 cups of sugar, but the baker only has 1/2 cup measuring cups. How many measuring cups does the baker need to measure out the sugar for the recipe?

We can start by converting the mixed number 1 3/4 into an improper fraction: 1 3/4 = 7/4. Then, we can divide 7/4 by 1/2:

7/4 ÷ 1/2 = 7/4 * 2/1 = 14/4 = 3 1/4

The baker needs 3 1/4 measuring cups to measure out the sugar for the recipe.

[Image: Three and a quarter measuring cups filled with sugar]

Step-by-step explanation:

Solution of 1 1/2 + 2 3/7 is 3 13/14

A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.

Given expression,

1 1/2 + 2 3/7

it can be written as

= 3/2 + 17/7

= (21 + 34)/14

= 55/14

= 3 13/14

Hence,  3 13/14 is the solution of 1 1/2 + 2 3/7

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Answer:

2w^2.

Step-by-step explanation:

Let "w" be the width of the walkway. Then, the length of the garden is 6.5(6x + 6) - 2w and the width of the garden is 6.5(6x + 6) - 2w.

The area of the garden is 6(4.5x + 2.5) = 6 * 4.5 * x + 6 * 2.5 = 27x + 15

The area of the garden and walkway is (6.5(6x + 6) - 2w)^2 = 27x + 15 + 2w^2

Equating the two expressions for the area of the garden:

27x + 15 = 27x + 15 + 2w^2

Thus, the area of the walkway is:

Answer:

Below

Step-by-step explanation:

According to the triangle bisector theorem

x/18 = 45/20

x = 40.5 units

On solving the provided question, we can say that ratio is = 2:5:7 => 2x + 5x + 7x = 84 => x =  6 and A gets = 2x = 12 rs.

Ratios show how often one number is contained in another in mathematics. For instance, the ratio of oranges to lemons in a fruit dish is 8 to 6 if there are 8 oranges and 6 lemons present. In a similar vein, the proportion of oranges to whole fruit is 8, while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b that is expressed as a / b, with b not equal to zero. An equation equating two ratios is known as a ratio. The ratio can be expressed as 1:3, for instance, if there is 1 boy and 3 girls (for every boy she has 3 girls) 3/4 are girls, while 1/4 are boys.

ratio is = 2:5:7

2x + 5x + 7x = 84

14x = 84

x = 84/14 = 6

a gets = 2x = 12 rs.

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The correlation between the amount of rain (mm) in the summer and the amount of water (m2) used for watering the lawn is directly proportion to each other

Based on the grain size, the classification of rain is divided into four, namely:

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The price of vase next year is $2090.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25

Given;

An antique vase costs $2000

Its price increases by 4.5%

Now,

Let the 4.5% of price be x

x*100/2000=4.5

x=20*4.5

x=90

Therefore, the price next year by 4.5 percent increase will be $2090.

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Answer:

Step-by-step explanation:

it equals 90

Han should expect to pay $90 for the ticket if he buys it the day of the game.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Han should expect to pay $90 for the ticket if he buys it the day of the game

The current ticket fee = $30

The markup = 200%

The markup = 200% of the current price

Markup = 200/100 ×30

= $60

The ticket fee on the game day = The current fee + The markup

The ticket fee on the game day = $30  +  $60

The ticket fee on the game day = $90

Hence, Han should expect to pay $90 for the ticket if he buys it the day of the game.

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Required  the equation of the line is y = -5/7 *x -4.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

the line through the point (7,-9) with slope -5/7

so, m= -5/7

now, y= mx+c

solving with the given values we get,

c=  -9 +5

 = -4

Hence, Required  the equation of the line is y = -5/7 *x -4.

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Answer:

a. To find the relative frequency of people that chose romance, we need to count the number of times the letter "R" appears in the given sequence and divide it by the total number of letters in the sequence.

The number of times "R" appears in the sequence is: R, R, R, R, R, R, H, R = 7

The total number of letters in the sequence is: 26

Relative frequency of people choosing romance = 7/26 = 0.269 or approximately 0.27.

b. To find the relative frequency of people that chose comedies, we need to count the number of times the letter "C" appears in the given sequence and divide it by the total number of letters in the sequence.

The number of times "C" appears in the sequence is: C, C, C, H, C, C, H, H, C, C = 9

The total number of letters in the sequence is: 26

Relative frequency of people choosing comedies = 9/26 = 0.346 or approximately 0.35.

c. To find the relative frequency of people that chose horror, we need to count the number of times the letter "H" appears in the given sequence and divide it by the total number of letters in the sequence.

The number of times "H" appears in the sequence is:

H, H, H, H, H, H, H = 7

The total number of letters in the sequence is: 26

Relative frequency of people choosing horror = 7/26 = 0.269 or approximately 0.27.

g. Based on the relative frequencies calculated, it can be seen that comedies is the most popular movie genre among the class, as it has the highest relative frequency of 0.35.

h. Based on the relative frequencies, it can be seen that romance is the least popular movie genre among the class, as it has the lowest relative frequency of 0.27. Hence, if we were having a party for the class, we would be least likely to pick romance as the genre of movie to watch.

The number of fifty dollars with the manager are 31.

Two or more expressions with an Equal sign is called as Equation.

Given that a convention manager finds that she has $1370, made up of twenties and fifties.

20x+50y=1370

She has a total of 46 bills.

x+y=46

x=46-y

Now we have to plug in x value in equation 1

20(46-y)+50y=1370

920-20y+50y=1370

920+30y=1370

Subtract 920 on both sides

30y=450

Divide both sides by 30

y=15

Now plug in y value in x+y=46

x+15=46

Subtract 15 on both sides

x=46-15

x=31

Hence, the number of fifty dollars with the manager are 31.

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Answer:

A

Step-by-step explanation:

the midsegment EF of the trapezoid ABCD is half the sum of the parallel bases, that is

EF = [tex]\frac{AB+DC}{2}[/tex] ( substitute values )

x + 6 = [tex]\frac{2x-9+x+5}{2}[/tex]

x + 6 = [tex]\frac{3x-4}{2}[/tex] ( multiply both sides by 2 to clear the fraction )

2x + 12 = 3x - 4 ( subtract 3x from both sides )

- x + 12 = - 4 ( subtract 12 from both sides )

- x = - 16 ( multiply both sides by - 1 )

x = 16

Then

EF = x + 6 = 16 + 6 = 22

The total amount to lay down the pebbles in the seating area would be - ${(A/5) x 8.99}.

Given is that one bag of pebbles covers 5 ft² and costs $8.99​​.

Assume that the area of the seating place is A ft². Now -

1 bag will cover - 5 ft²

1 ft² will be covered in (1/5) bags

A ft² will be covered in (A/5) bags

The total cost of laying the pebbles -

(A/5) x 8.99

Therefore, the total amount to lay down the pebbles in the seating area would be - ${(A/5) x 8.99}.

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The slope of the given situation of selling breakfast platters is 0.90.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

Given, the platter of 12 bagels costs $10.20.

The extra cost of  $4.65 for a gallon of coffee.

To find the slope of the situation, we convert the situation into the equation of the line.

y=mx+c

here c is the extra cost that is 4.65

12m=10.20

For 12 bagels , the cost is 10.20,

then the slope will be the cost of each bagel.

m=10.20/12

m=0.85

m=$0.85

Therefore, option c 0.85 is the slope of the given situation of the bakery selling the breakfast platter of 12 bagels and a gallon of coffee.

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In a market economy, option C. all consumers collectively have a great influence on the price of goods and services.

A market economy is an economic system in which goods and services are traded in a market, and prices are determined by supply and demand. The decisions of individual consumers and producers, operating through the market mechanism, determine what goods and services are produced and how they are distributed.

Therefore, the correct answer is as given above. It could be concluded that market economy allow individuals to influence the price of goods and services

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The answers to each part is given above.

Given is that when an object is thrown upward with an initial velocity of v{0}, then its approximate height is given by this quadratic function -

S = - 4.9t² + [tex]$v_{o} ^{t}[/tex] + h

The approximate height is given by this quadratic function -

S = - 4.9t² + [tex]$v_{o} ^{t}[/tex] + h

{ 1 } - For the maximum height :

dS/dt = 0                                        ... Eq{ 1 }

dS/dt = -9.8t + [tex]$3.1^{t}[/tex] log(3.1) + 0 = 0

- 9.8t + [tex]$3.1^{t}[/tex] log(3.1) = 0

Refer to the graph attached. At t = 3.8 {possible value}, the function is 0.

So we get -

t = 3.8 s                                         ... Eq{ 2 }  

Maximum height achieved -

h{max} = - 9.8t + [tex]$3.1^{t}[/tex] log(3.1) + 15

h{max} = - 9.8 x 3.8 + [tex]$3.1^{3.8}[/tex] log(3.1) + 15

h{max} =  - 37.24 + 73.65 x 0.50 + 15

h{max} =  14.585 m

{ 2 } -

0 = 3.1 t + 9.8/2 t²

0 = 3.1 t + 4.9 t²

Solving graphically, we get -

|t| = 0.6 s

Total time taken to reach ground -

T = 2 x 3.8 + 0.6

T = 8.2 seconds                                       ... Eq{ 3 }

Therefore, the answers to each part is given above.

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Answer:

1 quarter, 3 dimes, 1 nickel, 1 penny

Step-by-step explanation:

25c + 10c+10c+10c+5c+1c =61c

The cost of the packs of cards that Mike bought can be calculated by adding up the value of the coins he used to pay for them.

1 quarter is worth 25 cents.

2 dimes are worth 2 * 10 cents = 20 cents.

4 nickels are worth 4 * 5 cents = 20 cents.

4 pennies are worth 4 cents.

So, the total value of the coins that Mike used to pay for the packs of cards is 25 + 20 + 20 + 4 = 69 cents.

Therefore, the cost of the packs of cards that Mike bought was 69 cents.

Answer:

7/15

Step-by-step explanation:

Answer:

[tex]2\frac{7}{8}[/tex]

Step-by-step explanation:

size 10 dress requires 2 1/4 yards of fabric while a jacket requires 1 5/8 yards so we add them

2 1/4+1 5/8

we make similar fractions and turn the denominator to 8

2 2/8+ 1 5/8

and now we can add the whole numbers first

2+1=3

now the fractions

2/8+5/8

7/8

final answer is 2 7/8

hopes this helps

Answer:

50

Step-by-step explanation:

The size of the crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route is 44000 people.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, the size of a crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route,

The number of people that can fit comfortably in a 6 feet by 6 feet area = 10

The ratio of the number of people per unit area = 10/(6 × 6) = 10/36

The area, A, occupied by the crowd = 5 feet × 3 mile × 2

3 miles = 15840 feet

∴ A = 5 feet × 15840 feet × 2 = 158400 ft²

We then have;

Number of people / 158400 = 10/36

Number of people = 44000

Hence, the size of the crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route is 44000 people.

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Answer: 241

300 / 3 = 100

321 / 3 = 107

241 / 3 = 80.333

8.910 / 3 = 2.97